Non-linear charged black holes
Abstract
Very strong electromagnetic fields are characterized by the appearance of non-linearities. In order to explore the consequences of such non-linearities we have solved exactly the combined gravitational non-linear electromagnetic field equations for a static and spherical symmetric spacetime, where the source of the curvature is a point electric charge. We have chosen a non-linear Lagrangian density in such a way that the Maxwell, the Born--Infeld, and the Heisenberg--Euler theories are included as particular cases. The general solution can represent a charged black hole with the same characteristics of the Reissner--Nordstrø m one (two horizons and timelike singularity), or it can have only one horizon and a spacelike singularity, as in the Schwarzschild solution.